Am I correct in assuming that an interplanetary fighter craft using existing technology, that functions exclusively in the vacuum of space, could be made inherently lighter, more maneuverable, more fuel efficient, needing to carry less fuel, and better armed, than such a craft that could function both in a vacuum and enter an atmosphere as well as make terrestrial landings?
Yes. It can be lighter and more nimble than a multi-purpose aerospace fighter. It can also be heavier and more nimble than a multi-purpose aerospace fighter.
1 - it doesn't need flight control surfaces / airfoils or their hydraulic and electrical control systems to fly in-atmosphere. Instead it just needs strategically placed RCS thrusters and their control systems / fuel supply (hydrazine, perhaps?). The only limitation to how fast you can rotate the frame with those thrusters is what the pilot and the components can withstand.
1A - Without the need for external protrusions (wings, stabilizers), you would be free to engineer a much stealthier shape than modern fighters. It might resemble a kind of abstract oblong egg shape with odd geometry? This means recessed weapons/sensors and internal bomb / missile bays, distributed antennas and cameras, etc.. maybe less heat efficient? Using today's stealth technology, freed from the need for wings you could engineer something basicaly invisible to radar. It wouldn't be missile bait if you can't aquire the target.
3 - It doesn't need re-entry ablative heat shielding for atmospheric interface. By definition this will free up more mass for payload, fuel or other mission systems. It's probably still a good idea to have some heat shielding, just incase it needs to aerobrake in some planetary body's upper atmosphere. It's possible you can also engineer a kind of armor that diffuses certain wavelenths of light, to add resistance to laser attack and reduce observability in other wavelenghts like Infrared.
Basically yes. If you substantially decrease the scope of a vehicle, you typically can design it to be much better at what's still in scope.
In particular, landing and taking of is a monumental challenge. Taking off takes somewhere around 8 km/s of delta-V. That is a tremendous amount of fuel, which is why rockets are so big. There's effort to try to make usable air-breathers which fly part of the way before turning into a rocket, but nothing has been developed yet.
Landing is also quite a feat. I don't believe we've ever had a spacecraft which didn't need to go for a complete checkup before being cleared to take off again. Decelerating from orbital speeds by dumping heat into the atmosphere is a brutal exercise. We typically rely on ablative materials and replace them as neccesary.
As for the rest of it, however, that depends entirely on the specs for what a craft has to do during a fight. A Falcon 9 can pull just under 6g. If your craft needs to be able to maneuver at 6g with worse vibe requirements, you may actually need more structure than our modern rockets.
Then again, there's also the question of interplanetary multi-month or multi-year missions in a vehicle that's small enough to be called a "fighter."
There many reasons in other answers, but I want to point out the major one:
You can travel to Mars and back (low orbit - low orbit) for the same amount of fuel as just to get to low Earth orbit, and still have some spare to get to the Moon orbit.
Interplanatery transition requier much less energy, than jumping out of gravity well.
Space is not an ocean, and there is no inherent need for "fighters". We use fighters on aircraft carriers because we are dealing with two different fluid mediums, but in space, the only advantage of a larger vehicle is more mass or volume.
A "space fighter" can effectively do away with the "spacecraft" altogether. the 1980 era "Brilliant Pebble" interceptor simply orbited in a "lifejacket".
1980 era Brilliant Pebble concept
For interplanetary operations, the Brilliant Pebble can be launched in an interplanetary orbit via a mass driver, or carried by a missile bus. Since the Rocket Equation can be summarized by saying "every gram counts", every effort to reduce the mass of the space vehicle results in increased performance.
So you are not going to see some variation of an F-16, a "Star Fury" from Bablyon 5 or even a LEM with missile racks, but an unromantic missile bus at best, or a swarm of individual Brilliant Pebbles on an interplanetary orbit at worst.
So for interplanetary warships in general, minimal mass is what is needed, and throwing small missile busses into interplanetary orbits via mass drivers, or towing them with light-sails is the unromantic but most realistic way to approach space warfare.
The structural strength of the spaceframe -- airframe equivalent spacecraft -- would need to handle as much G-force as the human pilot --- or robotic pilot -- could tolerate. And if we start with human pilots in modern aircraft then that exceeds the one g of our gravity well.
The surface of an interplanetary fighter that wasn't designed to enter an atmosphere would only need to be armored to protect key components from weapons fire. If the craft needed to operate in our atmosphere it would need to contend with air turbulence and would need to be streamlined to mitigate damage when transiting through atmospheres at high speeds.
So, it might be a little bit heavier since it would require more metal around it or more surface area covered with something.
But, there seem to be applications of plasmas to high-speed aircraft to mitigate things like surface resistance and turbulence and sonic booms, so maybe those technologies could use electrical forces to generate a plasma surrounding the spacecraft to reduce the aerodynamic forces acting on the spacecraft.
Depends on how you envision them performing in each environment:
Space does not reduce G-force of acceleration and turning; so, you'll need to build your fighter on a solid structure either way so you don't tear yourself apart. Although a space fighter does not fly in an atmosphere, it may need some significant armor to protect against point defenses, solar radiation, and/or micro-meteors. So unless your military doctrine is specifically ultra-light armor, then you should be able to survive in atmosphere without any extra weight for survivability.
Fuel may be a non-issue if you are future tech enough. An antimatter or cold-fusion reactor would be efficient enough that you would not need a significant fuel to mass for planetary takeoff and landing as long as you have a good energy based propulsion system to go with it.
As for flight, a space fighter does not inherently need wings, but dissipating heat in space is hard. Installing your thrusters on wing like pylons to keep too much heat from building in your delicate central systems and cockpit could be necessary. So, making those pylons multi-role may not be a big sacrifice. If you wish to largely ignore the heatsink issue, you could also design your fighter with vtol type propulsion so it does not need aerodynamic lift to fly, instead, it's more like a high performance helicopter when in atmosphere.
None of the answers above really address the realistic shape of fighting spacecraft. Some of them are just to aerodynamic. Spacecraft depend on thrust vectoring to get around and some can move using a reaction wheel. The shape of the space craft would be symmetrical or pod like with the ability to maximize the maneuverability from all angle. Dog fights would greatly differ in space and advantage would be to ability to turn the trajectory of the spacecraft over if they are shooting unguided projectiles.
Space craft this complex would have some kind of smart missile and the ability to decoy would also play a big part. Though the pictures imaginative and borrowed the space craft would be very ugly and note aerodynamic.
The space craft could be aerodynamic but less efficient in space per once.